Can two electrons have the same location?

Read and understand the question and the answer.

That had nothing to do with the subject. I didn't say the electron and its field didn't have mass. And mass is energy (a la E=MC^2 ), But the energy we are able to actually utilize and work with has to do with MOVING that field which Requires an external source of energy to provide.

We were not talking about destruction of the electron and its field in the scenario of the OP (or in the link you provided). just moving it, not converting its mass to energy. That is a different subject.

Here is the question asked in your link.
(the answer was just a long version of 'yes')

Getting back to my original argument, if X is at rest for every instant up to but not including midnight, and midnight is the first instant that X is moving, what does that imply?

In classical terms, F=MA (where F is force, M is mass, and A is acceleration. At midnight dF/dt is non-zero; thus dA/dt must be also. That is, differential acceleration is non-zero. But X is at the same location that it was prior to midnight, since no time has elapsed.

The real problem here is logical: how can X be said to be "moving" when it hasn't moved? The non-zero differential acceleration is a label that has to be attached because there is no time delay between the application of a force and an acceleration.

But the basic logical problem remains: there must be a "first instant" when X is in relative motion with respect to the reference position where it was at rest; yet in that first instant of "motion" it has not moved, because it hasn't had time to move. That is a simple logical contradiction which arises from the meaning of "at rest" and "moving".

In fact, "motion" implies changing position, so that motion is never possible in any "instant" since an instant has zero duration but movement is a change over time.

I would add that there is no such thing as an "instant"; this is a nothing posing as a something, a temporal point similar to an equally logically inconsistent spatial point. Discrete models of time don't resolve the contradiction since every minimum of time in such models is an interval of positive length (duration) and every such interval can be subdivided by virtue of the fact that an interval consists of a pair of end points, not coincident but separated by a distance.

How long is "now"? Motion can't by definition take place in an instant.

IOW, neither of us has time for this argument...

I said nothing about utilizing energy or moving electrons. I said that "an electron at rest" generates an electric field; that this field, being potential energy, has a mass equivalent according to Einstein's equation relating energy to mass; and that this electric field contributes to the inertial mass of the electron and is therefore part of the electron.

Tell me which part of this you disagree with, and why, since this is all part of the standard model of physics as it currently exists.

Now, if all of that is true, then electrons aren't localized except insofar as electric fields are localized; and furthermore, since electric fields co-determine each other through the wave interference effect, you can't even talk about "an" electron in any logically consistent way.

Then why did you use an article that was about nothing BUT moving them to attempt proving your point?

The article wasn't ONLY about moving electric fields. Just look at the form of the question:

" The original question was: An electric field stores energy. Energy has mass if I understand E=mc correctly..."

And look at the form of the answer:

"Physicist: You’re exactly right. The electric field has mass (or, at the very least you could say that it has inertia and attracts things gravitationally), because it carries energy. The energy density, K, of the electric field around a charge, q, is..."

That's plain enough: an electric field stores energy and has mass/inertia.

Also see this Feynman lecture on renormalization theory, which also mentions moving electrons but (not surprisingly) begins with unmoving electrons (and pay close attention to the sentence I've taken the liberty of placing in all-caps):

"First, we compute the energy of a charged particle. Suppose we take a simple model of an electron in which all of its charge [Math Processing Error] is uniformly distributed on the surface of a sphere of radius [Math Processing Error], which we may take to be zero for the special case of a point charge. Now let’s calculate the energy in the electromagnetic field. If the charge is standing still, there is no magnetic field, and the energy per unit volume is proportional to the square of the electric field. The magnitude of the electric field is [Math Processing Error], and the energy density is [Math Processing Error]. TO GET THE TOTAL ENERGY, WE MUST INTEGRATE THIS DENSITY OVER ALL SPACE."

http://feynmanlectures.caltech.edu/II_28.html

Note that "math processing error" seems to have been added by my cellphone: I can't imagine it's present in the original text!

P.S. Potential energy is negative (mathematically speaking), so I think the electric field decreases the mass of the electron as a whole.

The key word is 'stores' energy, not 'is' energy.

The confusion I think is that we are mixing classical physics and quantum physics. I prefer to stick with classical because we really don't understand enough at the quantum level to make sense of it.

In classical terms, I can control electrons with amazing precision and make them do whatever I want, any time I want. In quantum terms, I don't even know where the damn thing is.

True dat.

I think it was Feynman who said (something like): "If you understand QM, then you don't understand it."

Well, an electric field consists of photons, whether actual or virtual, doesn't it? Aren't photons energy? They don't have a rest mass.

If an electron is continuously emitting photons in the form of an electric field, but never loses mass and never runs down or stops emitting an electric field of a fixed strength determined by the inverse square law, what does that imply?

It seems to me that, in physics as in economics, there IS such a thing as a free lunch; and not only that, but nothing is possible without a free lunch. The law of conservation of energy ultimately relies on atoms and particles that are in effect perpetual motion devices, that possess an unlimited amount of energy.

How could it be otherwise? How could something ever come to exist if you can't get something from nothing?

I keep running up against contradictions at the borders and foundations of things. These are present in both classical and quantum physics, because they're fundamental logical problems. Any system of science that fails to reconcile basic elements of space, time, and change is just a castle in the clouds.

Very informative link.
Thanks.

Thank you Neo.

The three people posting most on this thread are making up "science" based on their own imaginations, which I suppose is fine, as long as no one else thinks that what they are talking about has anything to do with actual science.

I am wondering if there is anyone interested in the actual science between any of these topics... we could start another thread I suppose. And, we could use actual math!

I'm going to risk answering without Googling first and looking like a fool because some Phd. somewhere has probably proposed that fields do consist of photons but in my understanding of classical physics, fields, unless in motion, do not emit photons. We are speaking of fields as in electro static (like on the plates of a charged capacitor (i.e. excess electrons) or the magnetic field around a stationary magnet.

The field is there as a force (like a compressed spring) but it is not emiting any photons. But as soon as you MOVE the field the story is different. But any 'energy' contained in the moving field is energy that came from an external source that caused the movement, not the field itself.

They are perpetual motion machines (ignoring the fact that if you wait long enough, all matter 'decays') only because they in effect have frictionless bearings. If you could harness the energy of their moving parts they would stop. If you harness the energy of their mass, they no longer exist other than as the photons to which they were converted to. But that is a very finite value, not unlimited.

The only 'free lunch' I'm aware of is the Big Bang. Other than that, there isn't one.

I wonder how many on a2k have that level of math/physics understanding. My background is pedestrian. And, though I understood your link quite well, I am hardly in a position to explain. When I was in high school, we pictured atoms as miniature solar systems. The electrons were little BBs flying around a core of billiard balls.

I wonder how many folks still labor under that impression. I suppose it bears little weight for everyday living, so long as you are not designing airplanes.

I have trouble understanding what "energy" is beyond being a theoretical abstraction invented for accounting purposes in balancing the mathematical books.

It's kinda like the term "mass." What is it?

F=MA, so M=F/A. So by definition it's basically a "resistance to acceleration." But what the hell is that? It isn't some "thing." It's a concept. It really doesn't refer to anything external that we can "explain" apart from the tautological implications of our verbal formulation.

That goes double for the concept of "potential energy" which is often treated as though it were "real energy."

Yeah.
Until you get hit in the head with a baseball.
Energy can have consequences

Well, sure, Neo. Just like Aristotleian "gravity" had consequences. You could see them every day. Things composed of the element "earth" would follow their "natural desires" to seek lower places. Fire would rise, etc.

After saying that, you know what gravity is, because it has consequences. Just jump out of a tall tree, and you'll find out what "gravity" is, sho nuff.

To those who are interested in actually doing things, it makes little difference whether electrons are orbiting the nucleus or appearing and then dissapearing only to reappear in a different spot at their assigned energy level (orbit). The model works.

PS: I designed airplanes and propulsion systems for them after my life as an EE and the exact mechanism for electron motion makes not one wit of difference to how they fly.

I take EE to mean "electrical engineer." It that accurate? If so..



does it make any (practical) difference in that field?

But you did use math, right?